Example 2.  For Example 3, compare the accuracy of the Trapezoidal Rule, Simpson's Rule, Simpson's Rule and Boole's Rule, with the Gauss-Legendre quadrature rules for n = 2, 3, 4 and 5 points, respectively.

Solution 2.

In all four cases, Gauss-Legendre quadrature is more accurate.

(c) John H. Mathews 2004